I have large files (several MB) and somehow my WiFi transfer is only up to 15KB/s. I wonder if doing DEFLATE compression is possible at all on Arduino:

What type of data? There might be easier ways to compress it; Huffman, Run-length, DPCM, etc. Otherwise porting one of the many implementations of DEFLATE is an interesting challenge as they often use many times the memory (SRAM) available in a typical Arduino ;-)

Yes this is the type of text data that DEFLATE loves. Only a fraction of the ASCII symbols are used and there are many common sequences.

As the number of symbols are low you could use BCD for numbers and the extra 10..15 value for special characters and run-length of zero which is very common. This way the compression rate should be 3-2:1 with a very simple algorithm. This will require a 8-bit binary format and a decoding program on the "other size".

As the symbols are known a simple version of DEFLATE could be constructed that used a much smaller encoding table. But still the limited memory in Arduino is a problem. A Mega could give enough to work with (8 Kbyte).